Simplify (y^4z^2)(y^-3z^-5)

$(y^{4} z^{2}) (y^{- 3} z^{- 5})$

Step 1

Multiply $y^{4}$ by $y^{- 3}$ by adding the exponents.

Move $y^{- 3}$ .

$y^{- 3} y^{4} z^{2} z^{- 5}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y^{- 3 + 4} z^{2} z^{- 5}$

Add $- 3$ and $4$ .

$y^{1} z^{2} z^{- 5}$

Step 2

Simplify $y^{1} z^{2} z^{- 5}$ .

$y z^{2} z^{- 5}$

Step 3

Multiply $z^{2}$ by $z^{- 5}$ by adding the exponents.

Move $z^{- 5}$ .

$y (z^{- 5} z^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y z^{- 5 + 2}$

Add $- 5$ and $2$ .

$y z^{- 3}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y \frac{1}{z^{3}}$

Step 5

Combine $y$ and $\frac{1}{z^{3}}$ .

$\frac{y}{z^{3}}$